# AL wire

What is the weight of an aluminum wire 250 m long with a diameter of 2 mm, if the density of aluminum is p = 2700 kg/m cubic. Determine to the nearest gram.

Result

m =  21 g

#### Solution:

$l=250 \ \text{m} \ \\ D=2 \ mm \rightarrow cm=2 / 10 \ cm=0.2 \ cm \ \\ ρ=2700 \ kg/m^3 \rightarrow g/cm^3=2700 / 1000 \ g/cm^3=2.7 \ g/cm^3 \ \\ \ \\ r=D/2=0.2/2=\dfrac{ 1 }{ 10 }=0.1 \ \text{cm} \ \\ S=\pi \cdot \ r^2=3.1416 \cdot \ 0.1^2 \doteq 0.0314 \ \text{cm}^2 \ \\ V=S \cdot \ l=0.0314 \cdot \ 250 \doteq 7.854 \ \text{cm}^3 \ \\ \ \\ m=ρ \cdot \ V=2.7 \cdot \ 7.854 \doteq 21.2058 \doteq 21 \ \text{g}$

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